A proof of the integral identity conjecture, II

Quy Thuong Lê

doi:10.1016/j.crma.2017.10.005

Logic/Algebraic geometry

A proof of the integral identity conjecture, II

Presented by: Claire Voisin

Quy Thuong Lê ^1,²

¹ Department of Mathematics, Vietnam National University, 334 Nguyen Trai Street, Hanoi, Viet Nam
² Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain

Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1041-1045.

Abstract
Résumé

In this note, using Cluckers–Loeser's theory of motivic integration, we prove the integral identity conjecture with framework a localized Grothendieck ring of varieties over an arbitrary base field of characteristic zero.

Dans cette note, en utilisant la théorie de l'intégration motivique de Cluckers et Loeser, nous prouvons la conjecture de l'identité intégrale dans le cadre d'un anneau de Grothendieck de variétés localisé sur un corps arbitraire de caractéristique nulle.

Received: 2017-07-17
Accepted: 2017-10-12
Published online: 2017-10-01

DOI: 10.1016/j.crma.2017.10.005

Author's affiliations:

Quy Thuong Lê ^{1, 2}

¹ Department of Mathematics, Vietnam National University, 334 Nguyen Trai Street, Hanoi, Viet Nam
² Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain

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     title = {A proof of the integral identity conjecture, {II}},
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Quy Thuong Lê. A proof of the integral identity conjecture, II. Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1041-1045. doi : 10.1016/j.crma.2017.10.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.10.005/

References
Cited by

[1] R. Cluckers; F. Loeser Constructible motivic functions and motivic integration, Invent. Math., Volume 173 (2008) no. 1, pp. 23-121

[2] J. Denef; F. Loeser Motivic Igusa zeta functions, J. Algebraic Geom., Volume 7 (1998), pp. 505-537

[3] J. Denef; F. Loeser Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math., Volume 135 (1999), pp. 201-232

[4] M. Kontsevich; Y. Soibelman Stability structures, motivic Donalson–Thomas invariants and cluster tranformations | arXiv

[5] Q.T. Lê On a conjecture of Kontsevich and Soibelman, Algebra Number Theory, Volume 6 (2012) no. 2, pp. 389-404

[6] Q.T. Lê Proofs of the integral identity conjecture over algebraically closed fields, Duke Math. J., Volume 164 (2015) no. 1, pp. 157-194

[7] J. Nicaise; S. Payne A tropical motivic Fubini theorem with applications to Donaldson–Thomas theory | arXiv

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